3
votes

Accepted

### On the Artin-Rees Lemma for non-commutative rings

There is some discussion of this in Rowen's "Ring Theory", volume I, Section 3.5, with additional references therein.
Exercise 19 on p. 462 in op. cit. states that a polycentral ideal $I$ of ...

3
votes

Accepted

### Invariants of general linear groups under torus action

Call the two matrices ${}_1A$ and ${}_2A$.
Your ring can be expressed by taking the $T$-invariants of the free ring in $2n^2$ variables $\mathbb C[{}_kA_{ij}]_{1\leq i,j\leq n, 1\leq k \leq 2}$ and ...

1
vote

### On the definition of the Cherednik algebra of a variety with a finite group action

Questions 2. and 3. are correct. By Cartan's Lemma $Y$ is smooth. For a point $p\in Y$ one has
$$T_{p}Y=(T_{p}X)^{g}\text{.}$$
If $1-\lambda_{Y,g}(p)=0$ then the action of $g$ on $T_{p}X$ is trivial. ...

1
vote

Accepted

### Prove that $\overline{a}_{11}$ is a prime element in $R$

Now that I have thought about this further, I realize that you need much less than the Samuel Conjecture to solve this problem. By a dimension count, the ring $R$ is a complete intersection ring, ...

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